// 奥数难度题库 - 巧算技巧类（1-50题）
const olympiadQuestions_part1 = [
  {
    id: 1,
    text: "小明发现一个计算规律：1.25×8=10，2.5×4=10，你能用这个规律快速计算1.25×3.2×2.5吗？",
    calculation: "1.25×3.2×2.5 = 1.25×(0.8×4)×2.5 = (1.25×0.8)×(4×2.5) = 1×10 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 分解因数凑整示例"
  },
  {
    id: 2,
    text: "聪聪在计算时发现：0.8×1.25=1，0.4×2.5=1，你能用这些规律快速计算0.8×1.25×4.8×2.5吗？",
    calculation: "0.8×1.25×4.8×2.5 = (0.8×1.25)×(0.4×2.5)×12 = 1×1×12 = 12",
    answer: 12,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 分解因数凑整拓展"
  },
  {
    id: 3,
    text: "老师告诉大家：2.5×0.4=1，1.25×0.8=1，你能用这些规律快速计算2.5×7.2×1.25吗？",
    calculation: "2.5×7.2×1.25 = 2.5×(0.4×18)×1.25 = (2.5×0.4)×(1.25×18) = 1×22.5 = 22.5",
    answer: 22.5,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 分解因数凑整练习"
  },
  {
    id: 4,
    text: "小华发现：0.5×2=1，0.25×4=1，0.125×8=1，你能用这些规律快速计算0.5×1.6×0.25×4.8×0.125吗？",
    calculation: "0.5×1.6×0.25×4.8×0.125 = (0.5×1.6)×(0.25×4.8)×(0.125×8)×0.6 = 0.8×1.2×1×0.6 = 0.576",
    answer: 0.576,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 多重凑整规律"
  },
  {
    id: 5,
    text: "通过观察，小丽发现1.1×1.1=1.21，1.1×1.2=1.32，1.1×1.3=1.43，她总结出一个规律：一个数乘1.1，积的规律为'首尾不变，中间相加'。你能用这个规律快速计算1.1×4.56吗？",
    calculation: "1.1×4.56 = 5.016（首尾为5和6，中间4+5=9，但需进位）",
    answer: 5.016,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律应用"
  },
  {
    id: 6,
    text: "小刚发现1.1×1.1=1.21，1.11×1.11=1.2321，1.111×1.111=1.234321，你能根据这个规律写出1.1111×1.1111的结果吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 小数乘法规律探究"
  },
  {
    id: 7,
    text: "通过计算1÷9=0.111…，2÷9=0.222…，3÷9=0.333…，小明发现规律。你能根据这个规律快速计算0.444…×9吗？",
    calculation: "0.444…×9 = 4",
    answer: 4,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数规律应用"
  },
  {
    id: 8,
    text: "小红计算了0.111…×9=1，0.222…×9=2，0.333…×9=3，她发现了一个规律。你能用这个规律快速计算0.123×9吗？",
    calculation: "0.123×9 = 1.107",
    answer: 1.107,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数规律拓展"
  },
  {
    id: 9,
    text: "小明发现5×2=10，25×4=100，125×8=1000，你能用这个规律快速计算12.5×0.8吗？",
    calculation: "12.5×0.8 = (125×0.1)×(8×0.1) = (125×8)×(0.1×0.1) = 1000×0.01 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值规律应用"
  },
  {
    id: 10,
    text: "通过观察1.5×2=3，0.75×4=3，0.375×8=3，你能用这个规律快速计算3.75×0.8吗？",
    calculation: "3.75×0.8 = (3.75×2)×(0.8÷2) = 7.5×0.4 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 倍数关系规律"
  },
  {
    id: 11,
    text: "小华发现：0.2×5=1，0.4×2.5=1，0.8×1.25=1，你能用这些规律快速计算1.6×0.625吗？",
    calculation: "1.6×0.625 = (0.8×2)×(0.8×0.78125) = 0.8×0.8×2×0.78125 = 0.64×1.5625 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 互为倒数规律"
  },
  {
    id: 12,
    text: "通过计算1.1×1.1=1.21，1.11×1.11=1.2321，1.111×1.111=1.234321，你能发现其中的规律并计算1.11111×1.11111吗？",
    calculation: "1.11111×1.11111 = 1.2345654321",
    answer: 1.2345654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律"
  },
  {
    id: 13,
    text: "小明计算了1÷9=0.111…，2÷9=0.222…，3÷9=0.333…，4÷9=0.444…，他发现了一个规律。你能用这个规律快速计算0.555…×9吗？",
    calculation: "0.555…×9 = 5",
    answer: 5,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数规律深化"
  },
  {
    id: 14,
    text: "小红发现1.1×1.1=1.21，1.1×1.2=1.32，1.1×1.3=1.43，1.1×1.4=1.54，你能根据这个规律快速计算1.1×7.89吗？",
    calculation: "1.1×7.89 = 8.679",
    answer: 8.679,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律深化"
  },
  {
    id: 15,
    text: "通过观察0.5×2=1，2.5×0.4=1，12.5×0.08=1，你能用这个规律快速计算1.25×8吗？",
    calculation: "1.25×8 = (12.5×0.1)×(8) = 12.5×0.1×8 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值变换规律"
  },
  {
    id: 16,
    text: "小刚发现0.125×8=1，0.0625×16=1，0.03125×32=1，你能用这个规律快速计算0.25×4吗？",
    calculation: "0.25×4 = 1",
    answer: 1,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 幂次规律"
  },
  {
    id: 17,
    text: "通过计算1÷3=0.333…，2÷3=0.666…，你能用这个规律快速计算0.333…×6吗？",
    calculation: "0.333…×6 = (1÷3)×6 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 分数小数转换规律"
  },
  {
    id: 18,
    text: "小丽发现1.25×0.8=1，2.5×0.4=1，5×0.2=1，你能用这些规律快速计算6.25×0.16吗？",
    calculation: "6.25×0.16 = (1.25×5)×(0.8×0.2) = (1.25×0.8)×(5×0.2) = 1×1 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 复合凑整规律"
  },
  {
    id: 19,
    text: "通过观察1.11×1.11=1.2321，1.111×1.111=1.234321，你能发现规律并计算1.1111×1.1111吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律应用"
  },
  {
    id: 20,
    text: "小华发现0.1666…×6=1，0.333…×3=1，你能用这个规律快速计算0.1666…×12吗？",
    calculation: "0.1666…×12 = (0.1666…×6)×2 = 1×2 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环小数倍数规律"
  },
  {
    id: 21,
    text: "通过计算1.25×8=10，2.5×4=10，5×2=10，你能用这个规律快速计算25×0.4吗？",
    calculation: "25×0.4 = (5×5)×(2×0.2) = (5×2)×(5×0.2) = 10×1 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值重组规律"
  },
  {
    id: 22,
    text: "小明发现1.1×1.1=1.21，1.1×1.2=1.32，1.1×1.3=1.43，你能用这个规律快速计算1.1×9.99吗？",
    calculation: "1.1×9.99 = 10.989",
    answer: 10.989,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律极限应用"
  },
  {
    id: 23,
    text: "通过计算1÷7=0.142857…，你能发现循环节的规律并计算0.142857…×7吗？",
    calculation: "0.142857…×7 = 1",
    answer: 1,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 循环节规律"
  },
  {
    id: 24,
    text: "小红发现0.125×8=1，0.25×4=1，0.5×2=1，你能用这些规律快速计算1.25×80吗？",
    calculation: "1.25×80 = (0.125×10)×(8×10) = (0.125×8)×(10×10) = 1×100 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值放大规律"
  },
  {
    id: 25,
    text: "通过观察1.111×1.111=1.234321，你能发现规律并计算1.111111×1.111111吗？",
    calculation: "1.111111×1.111111 = 1.234567654321",
    answer: 1.234567654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律深化"
  },
  {
    id: 26,
    text: "小刚发现0.076923…×13=1（1÷13=0.076923…），你能用这个规律快速计算0.076923…×26吗？",
    calculation: "0.076923…×26 = (1÷13)×(13×2) = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 分数循环节规律"
  },
  {
    id: 27,
    text: "通过计算1.25×0.8=1，2.5×0.4=1，你能用这些规律快速计算3.75×0.2666…吗？（提示：0.2666…=4/15）",
    calculation: "3.75×0.2666… = 3.75×(4/15) = (15×0.25)×(4/15) = 0.25×4 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 分数小数混合规律"
  },
  {
    id: 28,
    text: "小丽发现1.1×1.1=1.21，1.11×1.11=1.2321，你能用这个规律快速计算1.1111111×1.1111111吗？",
    calculation: "1.1111111×1.1111111 = 1.23456787654321",
    answer: 1.23456787654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 长循环对称数规律"
  },
  {
    id: 29,
    text: "通过计算1÷11=0.090909…，2÷11=0.181818…，你能用这个规律快速计算0.272727…×11吗？",
    calculation: "0.272727…×11 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十一进制循环规律"
  },
  {
    id: 30,
    text: "小华发现0.5×2=1，0.25×4=1，0.125×8=1，你能用这些规律快速计算0.0625×16吗？",
    calculation: "0.0625×16 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 二进制幂次规律"
  },
  {
    id: 31,
    text: "通过观察1.1×1.1=1.21，1.1×1.2=1.32，1.1×1.3=1.43，你能发现规律并计算1.1×5.67吗？",
    calculation: "1.1×5.67 = 6.237",
    answer: 6.237,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律三位数应用"
  },
  {
    id: 32,
    text: "小明发现1.25×8=10，2.5×4=10，你能用这个规律快速计算12.5×0.8吗？",
    calculation: "12.5×0.8 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值移动规律"
  },
  {
    id: 33,
    text: "通过计算1÷6=0.1666…，你能用这个规律快速计算0.1666…×12吗？",
    calculation: "0.1666…×12 = (1÷6)×12 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 六进制循环规律"
  },
  {
    id: 34,
    text: "小红发现0.2×5=1，0.4×2.5=1，你能用这些规律快速计算0.8×1.25吗？",
    calculation: "0.8×1.25 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 互为倒数规律深化"
  },
  {
    id: 35,
    text: "通过观察1.111×1.111=1.234321，你能发现规律并计算1.11111×1.11111吗？",
    calculation: "1.11111×1.11111 = 1.2345654321",
    answer: 1.2345654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律四位数应用"
  },
  {
    id: 36,
    text: "小刚发现0.090909…×11=1，你能用这个规律快速计算0.090909…×22吗？",
    calculation: "0.090909…×22 = (1÷11)×(11×2) = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十一进制循环规律应用"
  },
  {
    id: 37,
    text: "通过计算1.25×0.8=1，2.5×0.4=1，你能用这些规律快速计算5×0.2吗？",
    calculation: "5×0.2 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 基础凑整规律"
  },
  {
    id: 38,
    text: "小丽发现1.1×1.1=1.21，你能用这个规律快速计算1.1×8.88吗？",
    calculation: "1.1×8.88 = 9.768",
    answer: 9.768,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律多位小数应用"
  },
  {
    id: 39,
    text: "通过计算1÷12=0.08333…，你能用这个规律快速计算0.08333…×24吗？",
    calculation: "0.08333…×24 = (1÷12)×24 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十二进制循环规律"
  },
  {
    id: 40,
    text: "小华发现0.1666…×6=1，你能用这个规律快速计算0.1666…×18吗？",
    calculation: "0.1666…×18 = (1÷6)×18 = 3",
    answer: 3,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 六进制循环规律应用"
  },
  {
    id: 41,
    text: "通过观察1.25×8=10，你能用这个规律快速计算125×0.08吗？",
    calculation: "125×0.08 = 10",
    answer: 10,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值对称规律"
  },
  {
    id: 42,
    text: "小明发现1.11×1.11=1.2321，你能用这个规律快速计算1.1111×1.1111吗？",
    calculation: "1.1111×1.1111 = 1.23454321",
    answer: 1.23454321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律五位数应用"
  },
  {
    id: 43,
    text: "通过计算1÷15=0.0666…，你能用这个规律快速计算0.0666…×30吗？",
    calculation: "0.0666…×30 = (1÷15)×30 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十五进制循环规律"
  },
  {
    id: 44,
    text: "小红发现0.125×8=1，你能用这个规律快速计算1.25×80吗？",
    calculation: "1.25×80 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值放大规律应用"
  },
  {
    id: 45,
    text: "通过观察1.1×1.1=1.21，你能用这个规律快速计算1.1×4.444吗？",
    calculation: "1.1×4.444 = 4.8884",
    answer: 4.8884,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 乘1.1规律重复数字应用"
  },
  {
    id: 46,
    text: "小刚发现0.0588235294117647…×17=1（1÷17=0.0588235294117647…），你能用这个规律快速计算0.0588235294117647…×34吗？",
    calculation: "0.0588235294117647…×34 = (1÷17)×34 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十七进制循环规律"
  },
  {
    id: 47,
    text: "通过计算1.25×0.8=1，你能用这个规律快速计算12.5×8吗？",
    calculation: "12.5×8 = 100",
    answer: 100,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 位值变换规律应用"
  },
  {
    id: 48,
    text: "小丽发现1.111×1.111=1.234321，你能用这个规律快速计算1.111111×1.111111吗？",
    calculation: "1.111111×1.111111 = 1.234567654321",
    answer: 1.234567654321,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 对称数规律六位数应用"
  },
  {
    id: 49,
    text: "通过计算1÷18=0.0555…，你能用这个规律快速计算0.0555…×36吗？",
    calculation: "0.0555…×36 = (1÷18)×36 = 2",
    answer: 2,
    type: "巧算技巧-规律探究",
    source: "5-1.md 奥赛难度 - 十八进制循环规律"
  },
  {
    id: 50,
    text: "小华发现0.0625×16=1，你能用这个规律快速计算0.125×8吗？",
    calculation: "0.125×8 = 1",
    answer: 1,
    type: "巧算技巧-分解因数凑整",
    source: "5-1.md 奥赛难度 - 二进制幂次规律应用"
  }
];